Fractional quiver W-algebras

Kimura, Taro; Pestun, Vasily

doi:10.1007/s11005-018-1087-7

Cited by 60 publications

(109 citation statements)

References 38 publications

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“…The toroidal isomorphism was first pointed out in [14], and the definition of the quantum toroidal algebra (or quantum affinization of the affine Lie algebra) of gl 1 was inspired by [15]; the toroidal isomorphism was also independently re-derived in a series of papers [16][17][18]. More recently, the construction of the quantum toroidal algebras was generalized further to arbitrary quiver diagrams in [19].…”

Section: Jhep04(2017)152mentioning

confidence: 99%

Higher spins and Yangian symmetries

Gaberdiel

Gopakumar

et al. 2017

J. High Energ. Phys.

122

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Abstract:The relation between the bosonic higher spin W ∞ [λ] algebra, the affine Yangian of gl 1 , and the SH c algebra is established in detail. For generic λ we find explicit expressions for the low-lying W ∞ [λ] modes in terms of the affine Yangian generators, and deduce from this the precise identification between λ and the parameters of the affine Yangian. Furthermore, for the free field cases corresponding to λ = 0 and λ = 1 we give closed-form expressions for the affine Yangian generators in terms of the free fields. Interestingly, the relation between the W ∞ modes and those of the affine Yangian is a non-local one, in general. We also establish the explicit dictionary between the affine Yangian and the SH c generators. Given that Yangian algebras are the hallmark of integrability, these identifications should pave the way towards uncovering the relation between the integrable and the higher spin symmetries.

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Section: Jhep04(2017)152mentioning

confidence: 99%

Higher spins and Yangian symmetries

Gaberdiel

Gopakumar

et al. 2017

J. High Energ. Phys.

122

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“…theory dual to the little string is a q-deformation of g-type Toda, which has a deformed W(g)-algebra symmetry, and is therefore not a CFT [41]; for an analysis in this deformed setting, see [42]. For our purposes, it will be enough to turn off that deformation and work with the usual Toda CFT and its W(g)-algebra symmetry; this is the counterpart to the m s to infinity limit in the (2, 0) little string description, which gives the (2, 0) 6d CFT.…”

Section: Jhep05(2017)082mentioning

confidence: 99%

Little string origin of surface defects

Haouzi

Schmid

2017

J. High Energ. Phys.

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We derive a large class of codimension-two defects of 4d N = 4 Super YangMills (SYM) theory from the (2, 0) little string. The origin of the little string is type IIB theory compactified on an ADE singularity. The defects are D-branes wrapping the 2-cycles of the singularity. We use this construction to make contact with the description of SYM defects due to Gukov and Witten [1]. Furthermore, we provide a geometric perspective on the nilpotent orbit classification of codimension-two defects, and the connection to ADEtype Toda CFT. The only data needed to specify the defects is a set of weights of the algebra obeying certain constraints, which we give explicitly. We highlight the differences between the defect classification in the little string theory and its (2, 0) CFT limit.

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“…The goal of this section is to show that our construction admits a generalization to a huge class of 3d N = 2 unitary quiver gauge theories and W q,t ( ) algebras of [73]. Let us start by recalling some algebraic definition from [73]. A quiver is a collection of nodes 0 and arrows 1 , see Fig.…”

Section: Generalization To Quiver Gauge Theoriesmentioning

confidence: 99%

“…Supersymmetric 5d unitary quiver gauge theories in the -background have an interesting class of observables known as qq-characters, which have been recently constructed in [70] (building on previous works [71,72]). In particular, it is shown in [73] that the qq-characters generate quiver W q,t symmetry algebras and Ward identities for 5d (extended) Nekrasov partition functions [74,75]. When 5d gauge theories can be engineered by M-theory compactifications on toric Calabi-Yau 3-folds [76,77] or type IIB ( p, q)-webs [78,79], one can also use the refined topological vertex formalism [80][81][82] to conveniently compute the 5d Nekrasov partition functions.…”

Section: Introductionmentioning

confidence: 99%

q-Virasoro Modular Double and 3d Partition Functions

Nedelin

Nieri

Zabzine

2017

Commun. Math. Phys.

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Abstract:We study partition functions of 3d N = 2 U(N ) gauge theories on compact manifolds which are S 1 fibrations over S 2 . We show that the partition functions are free field correlators of vertex operators and screening charges of the q-Virasoro modular double, which we define. The inclusion of supersymmetric Wilson loops in arbitrary representations allows us to show that the generating functions of Wilson loop vacuum expectation values satisfy two SL(2, Z)-related commuting sets of q-Virasoro constraints. We generalize our construction to 3d N = 2 unitary quiver gauge theories and as an example we give the free boson realization of the ABJ(M) model.

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Fractional quiver W-algebras

Abstract: We introduce quiver gauge theory associated with the non-simply-laced type fractional quiver, and define fractional quiver W-algebras by using construction of [1, 2] with representation of fractional quivers.1 The M-theory brane picture for A-series is rotated by 90 degrees.

Cited by 60 publications

References 38 publications

Higher spins and Yangian symmetries

Higher spins and Yangian symmetries

Little string origin of surface defects

q-Virasoro Modular Double and 3d Partition Functions

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